Category Archives: wealth and income distribution

The Class Struggle

This chart is about what kind of world we live in. It’s drawn from the official source of the US national income accounts – the Bureau of Economic Analysis (BEA).

The chart shows the shares of national income going to compensation of employees and to corporate profits of domestic industries (with inventory valuation and capital consumption adjustments).


Note the vertical axes. On the left, there is the axis for the share for employee compensation – the blue line – which varies from 53-59 percent. The share for profits, which is on the order of 5-10 percent, is on the right vertical axis.

There is a high negative correlation between these two series, approximately -0.85.

Also, the scale of the changes in the shares of each are roughly of the same size, although not exactly.

Finally, the turning points in corporate profits and employee compensation line up in almost every case.

It’s important to note that employee compensation and profits do not simply sum to 100 percent; there are other categories of national income, and these have lower correlations with employee compensation.

There is much lower correlation between employee compensation and the sum of interest plus rents – both key components of property income.

There is also less (negative) correlation between proprietors income, which is about the same size as the corporate profit share, and employee compensation (-0.55). Presumeably, this is because proprietors income includes more sole proprietorships and family businesses; also, because wages for these companies may be lower than the corporate sector.

Of course, corporate profits have gone ballistic since 2008-2009, outpacing the increase in proprietors income.


So what this looks like is that increases in corporate profits come out of the share paid to employees somehow. Shades of Karl Marx!

In titling a post like this, I proceed cautiously, thinking some of my mentors in economics years back – Ray Marshall, A.G. Hart, and, briefly, W.W. Rostow to name a few.

Rostow used to talk of a Social Compact forged between labor and business after World War II. Fewer strikes and more automatic wage increases. That clearly has ended.

The Distribution of Income and Wealth – Global Estimates

There’s a lot of buzz about Thomas Piketty’s work Capital in the Twenty-First Century which altogether runs 685 pages in the hardcover edition.

I’m reading it. It’s well written and, for the material, entertaining, with entertaining allusions and examples from literature and other media (TV, film). I’m not prepared or willing, at this point, to comment on key contentions – such as whether the rate of return on capital r tends historically to be greater than g, the overall growth rate of the economy. The basic finding that the distribution of wealth is growing significantly more unequal once, of course, is rock solid.

The following links fill in some of the contemporary context on income and wealth distribution, which might help if you read the book and which have clear implications for business and marketing, if you think things through and get the trends right.

Wealth is different from income, of course. Here is a graphic taking a swipe at estimating the global distribution of wealth (2012 OECD Forum).


The estimate here is there are, globally, about 29 million millionaires, as individuals. That estimate masks, of course, significant within-group differences, as is shown in the following detail on the apex of the pyramid.


Similarly, detail for the bottom of the global wealth pyramid, where average individual wealth is less than 10,000 US dollar equivalents, can be expanded.

Felix Salmon reports that the poorest 2 billion persons in the global population actually have negative net worth. So based on the data source for the above pyramids, the bottom 30 percent of global population has a negative net worth of about half a trillion dollar equivalents. They owe it to the company store, the landlord, to petty lenders, to Uncle Omar and so forth.

Note these charts are cast in terms of adults. The total global population currently is about 7.2 trillion so without making an exact translation, this means billions of children are being raised in extreme poverty.

In the US, about 50 percent of the US population is reported to have zero net wealth.

In 2006, about 4 trillion persons are estimated to subsist on less than $10 per day or an annual individual income of less than $3,650 a year in dollar equivalents. About 2.4 trillion persons in 2006 lived on less than $5 a day.

Some Implications

Electronics and especially cell phones intersect with these numbers in a dynamic way. The cell phone is a vital investment for some remote farming villages. Families can scrape together the $100 or so for an “inexpensive” phone and have a kind of business, renting it to members of the community to check prices in local markets, keep in touch with family, and so forth.

And, in general, declining unit prices of information processing mean that more and more of the global population is interconnected and have access, in some fashion, to global markets and communications.

Anyway, here is Thomas Piketty on economic inequality.

Top photo from


The “Hollowing Out” of Middle Class America

Two charts in a 2013 American Economic Review (AER) article put numbers to the “hollowing out” of middle class America – a topic celebrated with profuse anecdotes in the media.


The top figure shows the change in employment 1980-2005 by skill level, based on Census IPUMS and American Community Survey (ACS) data. Occupations are ranked by skill level, approximated by wages in each occupation in 1980.

The lower figure documents the changes in wages of these skill levels 1980-2005.

These charts are from David Autor and David Dorn – The Growth of Low-Skill Service Jobs and the Polarization of the US Labor Market – who write that,

Consistent with the conventional view of skill-biased technological change, employment growth is differentially rapid in occupations in the upper two skill quartiles. More surprising in light of the canonical model are the employment shifts seen below the median skill level. While occupations in the second skill quartile fell as a share of employment, those in the lowest skill quartile expanded sharply. In net, employment changes in the United States during this period were strongly U-shaped in skill level, with relative employment declines in the middle of the distribution and relative gains at the tails. Notably, this pattern of employment polarization is not unique to the United States. Although not recognized until recently, a similar “polarization” of employment by skill level has been underway in numerous industrialized economies in the last 20 to 30 years.

So, employment and wage growth has been fastest in the past three or so decades (extrapolating to the present) in low skill and high skill occupations.

Among lower skill occupations, such as food service workers, security guards, janitors and gardeners, cleaners, home health aides, child care workers, hairdressers and beauticians, and recreational workers, employment grew 30 percent 1980-2005.

Among the highest paid occupations – classified as managers, professionals, technicians, and workers in finance, and public safety – the share of employment also grew by about 30 percent, but so did wages – which increased at about double the pace of the lower skill occupations over this period.

Professor Autor is in the MIT economics department, and seems to be the nexus of a lot of interesting research casting light on changes in US labor markets.


In addition to “doing Big Data” as the above charts suggest, David Autor is closely associated with a new, common sense model of production activities, based on tasks and skills.

This model of the production process, enables Autor and his coresearchers to conclude that,

…recent technological developments have enabled information and communication technologies to either directly perform or permit the offshoring of a subset of the core job tasks previously performed by middle skill workers, thus causing a substantial change in the returns to certain types of skills and a measurable shift in the assignment of skills to tasks.

So it’s either a computer (robot) or a Chinaman who gets the middle-class bloke’s job these days.

And to drive that point home – (and, please, I consider the achievements of the PRC in lifting hundreds of millions out of extreme poverty to be of truly historic dimension) Autor with David Dorn and Gordon Hansen publihsed another 2013 article in the AER titled The China Syndrome: Local Labor Market Effects of Import Competition in the United States.

This study analyzes local labor markets and trade shocks to these markets, according to initial patterns of industry specialization.

The findings are truly staggering – or at least have been equivocated or obfuscated for years by special pleaders and lobbyists.

Dorn et al write,

The value of annual US goods imports from China increased by a staggering 1,156 percent from 1991 to 2007, whereas US exports to China grew by much less…. 

Our analysis finds that exposure to Chinese import competition affects local labor markets not just through manufacturing employment, which unsurprisingly is adversely affected, but also along numerous other margins. Import shocks trigger a decline in wages that is primarily observed outside of the manufacturing sector. Reductions in both employment and wage levels lead to a steep drop in the average earnings of households. These changes contribute to rising transfer payments through multiple federal and state programs, revealing an important margin of adjustment to trade that the literature has largely overlooked,

This research – conducted in terms of ordinary least squares (OLS), two stage least squares (2SLS) as well as “instrumental” regressions – is definitely not something a former trade unionist is going to ponder in the easy chair after work at the convenience store. So it’s kind of safe in terms of arousing the ire of the masses.

But I digress.

For my purposes here, Autor and his co-researchers put pieces of the puzzle in place so we can see the picture.

The US occupational environment has changed profoundly since the 1980’s. Middle class jobs have simply vanished over large parts of the landscape. More specifically, good-paying production jobs, along with a lot of other more highly paid, but routinized work, has been the target of outsourcing, often to China it seems it can be demonstrated. Higher paid work by professionals in business and finance benefits from complementarities with the advances in data processing and information technology (IT) generally. In addition, there are a small number of highly paid production workers whose job skills have been updated to run more automated assembly operations which seem to be the chief beneficiaries of new investment in production in the US these days.

There you have it.

Market away, and include these facts in any forecasts you develop for the US market.

Of course, there are issues of dynamics.

Links – April 26, 2014

These Links help orient forecasting for companies and markets. I pay particular attention to IT developments. Climate change is another focus, since it is, as yet, not fully incorporated in most longer run strategic plans. Then, primary global markets, like China or the Eurozone, are important. I usually also include something on data science, predictive analytics methods, or developments in economics. Today, I include an amazing YouTube of an ape lighting a fire with matches.


Xinhua Insight: Property bubble will not wreck China’s economy

Information Technology (IT)

Thoughts on Amazon earnings for Q1 2014


This chart perfectly captures Amazon’s current strategy: very high growth at 1% operating margins, with the low margins caused by massive investment in the infrastructure necessary to drive growth. It very much feels as though Amazon recognizes that there’s a limited window of opportunity for it to build the sort of scale and infrastructure necessary to dominate e-commerce before anyone else does, and it’s scraping by with minimal margins in order to capture as much as possible of that opportunity before it closes.

Apple just became the world’s biggest-dividend stock


The Disruptive Potential of Artificial Intelligence Applications Interesting discussion of vertical search, virtual assistants, and online product recommendations.

Hi-tech giants eschew corporate R&D, says report

..the days of these corporate “idea factories” are over according to a new study published by the American Institute of Physics (AIP). Entitled Physics Entrepreneurship and Innovation (PDF), the 308-page report argues that many large businesses are closing in-house research facilities and instead buying in new expertise and technologies by acquiring hi-tech start-ups.

Climate Change

Commodity Investors Brace for El Niño

Commodities investors are bracing themselves for the ever-growing possibility for the occurrence of a weather phenomenon known as El Niño by mid-year which threatens to play havoc with commodities markets ranging from cocoa to zinc.

The El Niño phenomenon, which tends to occur every 3-6 years, is associated with above-average water temperatures in the central and eastern Pacific and can, in its worst form, bring drought to West Africa (the world’s largest cocoa producing region), less rainfall to India during its vital Monsoon season and drier conditions for the cultivation of crops in Australia.


Researchers Tested The ‘Gambler’s Fallacy’ On Real-Life Gamblers And Stumbled Upon An Amazing Realization I love this stuff. I always think of my poker group.

..gamblers appear to be behaving as though they believe in the gambler’s fallacy, that winning or losing a bunch of bets in a row means that the next bet is more likely to go the other way. Their reactions to that belief — with winners taking safer bets under the assumption they’re going to lose and losers taking long-shot bets believing their luck is about to change — lead to the opposite effect of making the streaks longer

Foreign Affairs Focus on Books: Thomas Piketty on Economic Inequality

Is the U.S. Shale Boom Going Bust?

Among drilling critics and the press, contentious talk of a “shale bubble” and the threat of a sudden collapse of America’s oil and gas boom have been percolating for some time. While the most dire of these warnings are probably overstated, a host of geological and economic realities increasingly suggest that the party might not last as long as most Americans think.

Apes Can Definitely Use Tools

Bonobo Or Boy Scout? Great Ape Lights Fire, Roasts Marshmallows


Power Laws

Zipf’s Law

George Kingsley Zipf (1902-1950) was an American linguist with degrees from Harvard, who had the distinction of being a University Lecturer – meaning he could give any course at Harvard University he wished to give.

At one point, Zipf hired students to tally words and phrases, showing, in a long enough text, if you count the number of times each word appears, the frequency of words is, up to a scaling constant, 1/n, where n is the rank. So second most frequent word occurs approximately ½ as often as the first; the tenth most frequent word occurs 1/10 as often as the first item, and so forth.

In addition to documenting this relationship between frequency and rank in other languages, including Chinese, Zipf discussed applications to income distribution and other phenomena.

More General Power Laws

Power laws are everywhere in the social, economic, and natural world.

Xavier Gabaix with NYU’s Stern School of Business writes the essence of this subject is the ability to extract a general mathematical law from highly diverse details.

For example, the that an animal of mass M requires to live is proportional to M3/4. This empirical regularity… has been explained only recently .. along the following lines: If one wants to design an optimal vascular system to send nutrients to the animal, one designs a fractal system, and maximum efficiency exactly delivers the M3/4 law. In explaining the relationship between energy needs and mass, one should not become distracted by thinking about the specific features of animals, such as feathers and fur. Simple and deep principles underlie the regularities.


This type of relationship between variables also characterizes city population and rank, income and wealth distribution, visits to Internet blogs and blog rank, and many other phenomena.

Here is the graph of the power law for city size, developed much earlier by Gabaiux.


There are many valuable sections in Gabaix’s review article.

However, surely one of the most interesting is the inverse cubic law distribution of stock price fluctuations.

The tail distribution of short-term (15 s to a few days) returns has been analyzed in a series of studies on data sets, with a few thousands of data points (Jansen & de Vries 1991, Lux 1996, Mandelbrot 1963), then with an ever increasing number of data points: Mantegna& Stanley (1995) used 2 million data points, whereas Gopikrishnan et al. (1999) used over 200 million data points. Gopikrishnan et al. (1999) established a strong case for an inverse cubic PL of stock market returns. We let rt denote the logarithmic return over a time interval.. Gopikrishnan et al. (1999) found that the distribution function of returns for the 1000 largest U.S. stocks and several major international indices is


This relationship holds for positive and negative returns separately.

There is also an inverse half-cubic power law distribution of trading volume.

All this is fascinating, and goes beyond a sort of bestiary of weird social regularities. The holy grail here is, as Gabaix says, robust, detail-independent economic laws.

So with this goal in mind, we don’t object to the intricate details of the aggregation of power laws, or their potential genesis in proportional random growth. I was not aware, for example, that power laws are sustained through additive, multiplicative, min and max operations, possibly explaining why they are so widespread. Nor was I aware that randomly assigning multiplicative growth factors to a group of cities, individuals with wealth, and so forth can generate a power law, when certain noise elements are present.

And Gabaix is also aware that stock market crashes display many attributes that resolve or flow from power laws – so eventually it’s possible general mathematical principles could govern bubble dynamics, for example, somewhat independently of the specific context.

St. Petersburg Paradox

Power laws also crop up in places where standard statistical concepts fail. For example, while the expected or mean earnings from the St. Petersburg paradox coin flipping game does not exist, the probability distribution of payouts follow a power law.

Peter offers to let Paul toss a fair coin an indefinite number of times, paying him 2 coins if it comes up tails on the first toss, 4 coins if the first head comes up on the second toss, and 2n, if the first head comes up on the nth toss.

The paradox is that, with a fair coin, it is possible to earn an indefinitely large payout, depending on how long Paul is willing to flip coins. At the same time, behavioral experiments show that “Paul” is not willing to pay more than a token amount up front to play this game.

The probability distribution function of winnings is described by a power law, so that,

There is a high probability of winning a small amount of money. Sometimes, you get a few TAILS before that first HEAD and so you win much more money, because you win $2 raised to the number of TAILS plus one. Therefore, there is a medium probability of winning a large amount of money. Very infrequently you get a long sequence of TAILS and so you win a huge jackpot. Therefore, there is a very low probability of winning a huge amount of money. These frequent small values, moderately often medium values, and infrequent large values are analogous to the many tiny pieces, some medium sized pieces, and the few large pieces in a fractal object. There is no single average value that is the characteristic value of the winnings per game.

And, as Liebovitch and Scheurle illustrate with Monte Carlo simulations, as more games were played, the average winnings per game of the fractal St. Petersburg coin toss game …increase without bound.

So, neither the expected earnings nor the variance of average earnings exists as computable mathematical entities. And yet the PDF of the earnings is described by the formula Ax-α  where α is near 1.

Closing Thoughts

One reason power laws are so pervasive in the real world is that, mathematically, they aggregate over addition and multiplication. So the sum of two variables described by a power law also is described by a power law, and so forth.

As far as their origin or principle of generation, it seems random proportional growth can explain some of the city size, wealth and income distribution power laws. But I hesitate to sketch the argument, because it seems somehow incomplete, requiring “frictions” or weird departures from a standard limit process.

In any case, I think those of us interested in forecasting should figure ways to integrate these unusual regularities into predictions.